Atmospheric Optics Glossary

This doesn't pretend to be complete. It does try to explain technical
terms used in my green-flash/mirage/refraction pages. These terms are
drawn from a variety of disciplines: optics, meteorology, astronomy,
hydrography, navigation, geodesy, etc.

Links in italics refer to other terms in this Glossary.
Links in boldface refer to the
bibliography.

If you can't find a term here, try the
alphabetical index.
If you still can't find it, please
write to me
and ask that the missing term(s) be added.

A

AEROSOL refers to small particles suspended in the air, as opposed to big
“hydrometeors” like snowflakes and raindrops.
Aerosols make the air look
hazy by scattering light; the loss of light
by scattering increases the atmospheric
extinction.

The relative AIRMASS is the ratio of the amount of air in the line of
sight (at some zenith distance Z) to the amount in the zenith.
It gives the relative amounts of molecular
extinction at different zenith distances.

ALTITUDE: Angular distance above (positive) or below (negative) the
horizontal (i.e., the
astronomical horizon.)
Altitude is usually measured in degrees and
minutes of arc.

This is the astronomical definition of the term. In common usage,
“altitude”, “elevation”, “height”
and the like are used
indiscriminately for both angular and linear measurements; and the
technical usage varies from one field to another. Be aware of possible
confusion here.

Because altitude is the coordinate affected by refraction, it's usual
to distinguish between apparent altitude (the observed quantity,
affected by atmospheric refraction) and true or geometric altitude
(where an object would appear without the effect of refraction).

APPARENT HORIZON: Where the sky appears to meet the Earth.
(See also sea horizon.)
Because of perspective effects, different observers generally have
different apparent horizons.
Because of
refraction, even the
sea horizon
usually lies above the
geometric horizon.

ASTRONOMICAL HORIZON: the intersection of a horizontal plane through the
eye with the
celestial sphere.
(NOTE: because the celestial sphere has an
infinite radius, two
observers at different heights above sea level, but placed on the same
vertical line, have the same astronomical horizon.)
Because of
dip,
the astronomical horizon always lies above the
sea horizon.
But it usually is hidden by trees, hills, and buildings on land.
These objects then determine the observer's apparent horizon (see above).

ASTRONOMICAL REFRACTION: The displacements of astronomical objects by
atmospheric refraction. The effect is about a
minute of arc
at 45° from the
zenith, and increases roughly with the
tangent of the
zenith distance;
at the horizon, it is typically about half
a degree, and quite variable. These effects are many orders of magnitude
larger than the accuracy of the best astronomical position measurements,
and so large that the mountings of most astronomical telescopes are
adjusted to minimize the effects of refraction. See also
terrestrial refraction.

B

BOUNDARY LAYER: A relatively thin layer of fluid next to a boundary
(such as a solid surface).
Example: the layer of air next to the Earth's surface (the “planetary
boundary layer”). Ordinarily, only the boundary layer is appreciably
affected by the properties of the surface. The rest of the fluid is
unaffected; so the part of the atmosphere above the boundary layer
(which is typically a few hundred meters thick) is called the “free
atmosphere.”

BOUNDARY LAYER METEOROLOGY is the name of the discipline that studies
atmospheric boundary layers, as well as the name of a leading journal in
this field.

C

CELESTIAL SPHERE: An imaginary sphere of infinite radius, centered at the
observer. A point on the celestial sphere is really only a direction in
space; parallel lines meet the celestial sphere in the same point.

CREPUSCULAR RAYS: When the lower atmosphere is hazy, light passing through
gaps between broken clouds can produce bright “beams” that are made
visible by scattering by
aerosol particles. These are usually seen best
when the Sun is low, or at twilight (hence the term “crepuscular.”)

D

DENSITY: How much stuff there is in how much space. The density of water
is 1 gram per cubic centimeter, or one (metric) ton per cubic meter.
The density of air is about 1 kilogram per cubic meter — about a thousand
times less dense than water.
The density of air is proportional to its pressure, and inversely
proportional to its (absolute) temperature.

DISPERSION: The variation of
refraction, or refractive index,
with the wavelength or color of light. All transparent media — air,
water, glass, etc. — are dispersive. Normally, the refraction is greater
for the short wavelengths (blue and violet) and least for the long ones
(red light). See my dispersion page
for details.

DUCT: If the ray curvature within a
thermal inversion
is stronger than the curvature of the Earth's surface, rays can be
continuously guided
along the surface of the Earth without ever escaping
to space. This region in which rays are trapped is called a duct.
An observer within the duct sees a
superior mirage
of distant objects within the duct.
Ducting occurs when the temperature
gradient within the inversion is
steeper than about 10 K in 100 meters (1 degree in 10 m).
See the
duct page
for details.

E

EXTINCTION: loss of light in the atmosphere.
Extinction is the sum of
actual absorption, and scattering.

F

FATA MORGANA: A complex mirage
display that involves multiple images, alternately expanded and compressed
vertically, often giving the impression of buildings, cliffs, etc. where
no such objects exist. The name is traditionally used in Italy for
the vivid mirages seen across the Strait of Messina.

G

GEODESY is the study of the size and shape of the Earth.
The corresponding adjective is geodetic.

GEOID is the equipotential surface corresponding to mean sea level.
NOAA
has a nice discussion of this term.

GEOMETRIC HORIZON: Where the apparent sea horizon would be if
there were no refraction; equivalently, where the cone with vertex at the
observer's eye and tangent to the sea surface would meet the
celestial sphere.

GRADIENT: the rate at which something changes; here, we are talking about
temperature gradients: how fast the temperature changes with
height
in the atmosphere.
The
bending
of rays in the atmosphere depends on the temperature gradient.

GREEN FLASHes are phenomena seen at sunrise and sunset,
when some part of the Sun suddenly changes color (at sunset, from
red or orange to green or blue).
There are
several quite different phenomena
commonly lumped together under
the name of “the green flash”, and this intermingling of disparate
phenomena has fostered confusion.
So I prefer to say “green flashes” and avoid the definite article.
[See the
photographs
and
simulations.]

GREEN RAY: a rare kind of green flash, in which an actual beam of green
light is seen shooting up from the horizon where the Sun has just set,
or from the Sun itself. Usually this beam or ray is only a few times
larger than the Sun itself; sometimes, it appears as a diffuse glow.
I now have a separate page
on this topic. Unfortunately, the term “green ray” has often been used
for green flashes in general — a confusing practice that should be
discouraged.

GREEN RIM: When the Sun is low, normal atmospheric dispersion raises the
short-wavelength images of the Sun more than the long-wavelength images;
but atmospheric extinction
attenuates the blue so much that the upper edge
usually appears green, not blue or violet.
See the simulation
of a sunset in the
Standard Atmosphere.
The
green rim
is so narrow that it can only be seen telescopically.

GREEN SEGMENT: Mulder's term
(popularized by his followers
Minnaert and
O'Connell) for all the
common kinds
of green flash together.
This catch-all category is no longer useful, and should be avoided.

H

HEIGHT: Linear distance (usually measured in meters) above sea level;
as contrasted with
altitude, which is angular distance above the
astronomical horizon. Usually called
“elevation” by geographers.

I

INFERIOR MIRAGE: "Inferior" means "lower"; this is the mirage in which
the inverted image is below the normal one. The common example is
the hot-road mirage seen on sunny days.

INVERSION refers to something being upside down. Don't confuse inversion
of an image with inversion of the temperaturegradient
(a thermal inversion).

IRRADIANCE:
The amount of power per unit area in a beam of light.
Sometimes also called flux.
Units: W m-2

J

K

L

LAPSE RATE: The rate at which temperature decreases with
height
in the atmosphere. This has the opposite sign from the temperature
gradient a physicist would use, so be careful.

LATERAL MIRAGE: A much mis-used term. Refraction in the horizontal
direction is appreciable only when a boundary layer is stabilized by a
wall or other near-vertical surface; in such cases, the term
“mural mirage”
is more descriptive. (See
here
for further discussion.)

Unfortunately, the existence of the term “lateral mirage” has
encouraged uncritical observers to think they have seen images separated by
many degrees in azimuth from the actual direction to the object. These are
always cases of mis-identification; atmospheric refraction cannot produce
such effects.

LUMINANCE: The amount of visible light per unit area and per unit solid
angle. Often called “surface brightness”.
This is the visual quantity analogous to the radiometric quantity
radiance.

M

MINUTE: Don't confuse a minute of time with a
minute of arc.
A minute of time is 1/60 of an hour; a minute of arc is 1/60 of a degree.

MIRAGE: An inverted image caused by atmospheric refraction.

I'm surprised to find mirages defined in very different ways in
various reference books and dictionaries. Some are too restrictive,
and/or give incorrect explanations. Others run to the opposite extreme,
with definitions so broad as to include almost everything you see.

I consider a mirage to be any display of atmospheric
refraction that
produces either multiple images of an object, or at least one inverted
image. (It can be shown that these descriptions are essentially
equivalent; however, in practice, one or more of the multiple images may
be so compressed or distorted as to be unrecognizable.) There are many
kinds, including the classical
inferior
and
superior
mirages, the
mock mirage, and
Wegener's Nachspiegelung.
I now have a
mirage page
where these phenomena are explained more fully.
(Also, see the table of
refraction phenomena.)

MOCK MIRAGE: an inverted image produced by a
thermal inversion
below eye level. (See the
ray diagram on the
mirage page for details.)
While the classical inferior and superior mirages can be regarded, for
some purposes, as due to internal reflections, no such interpretation is
possible for the others, which might well be called “pseudo-mirages.”

Caution: terms like “mock mirage” and “pseudo-mirage” should not be
taken to mean that these phenomena are any less real than the classical
inferior and superior mirages. The names are chosen simply to distinguish
the recently-understood mirages from the classical ones, which involve
different optical mechanisms. See the ray diagrams on the
mirage page for an explanation of the
different kinds, and the table of
refraction phenomena.

MURAL MIRAGE: A mirage produced by the boundary layer of hot air next to a
heated or sunlit wall. It is essentially an
inferior mirage turned on its side.
See
here
for further discussion.

O

OPTICAL DEPTH:
If the transmission of a slab of material is t = exp(-τ)
then we say that τ is the optical depth of the material.
So the optical depth is the negative of the natural logarithm of the
transmission. (Note that it is a dimensionless number.)

A similar measure of opacity, called optical density, which is used
in photography, uses the common (base 10) logarithm instead of the
natural (base e) one. Don't confuse them.

P

PERIGEE: The point on a trajectory, or the path of a refracted ray,
that is nearest the center of the Earth.

PSEUDO-MIRAGE: A mirage that cannot be
explained, even approximately, as due to internal reflection at the
interface between warm and cool air. The
mock mirage and Wegener's
Nachspiegelung
are examples of pseudo-mirages.

Q

R

RADIANCE:
The amount of power per unit area and per unit solid angle
in a beam of light.
(Think of it as the
irradiance per unit solid angle.)
Units: W m-2 sterad-1

REFRACTION: the
bending
of rays of light in passing from one medium to
another (e.g., air to water), or between parts of the same medium with
different densities (e.g., different levels in the atmosphere). The
amount of refraction is given by Snel's law, which
is expressed in terms of the medium's refractive index, which is just
the ratio of the speed of light in a vacuum to that in the medium.
(See the
refraction
page.)

Don't confuse refraction (the process) with refractive index
(a ratio of propagation speeds), or the latter with refractivity
(which is the refractive index minus unity.)
In gases, it is an excellent approximation to set the refractivity
proportional to the density
of the gas. Things are more complicated for
dense materials like solids and liquids, however.

Also, don't confuse refraction with diffraction, which is
the spreading-out of light at the edge of a shadow. Diffraction is purely
a wave-optical phenomenon, and is appreciable only when the lateral
dimension of an object in the path of the light is only a few wavelengths.
Refraction is a ray-optical phenomenon that strictly is useful only when
objects are many wavelengths across. So the two phenomena are usually
important only in mutually exclusive situations. But, because the words
are similar, many people confuse the two terms.

S

SCATTERING: When light passes through a medium that is not perfectly
homogeneous, the irregularities in the medium scatter some of the light in
all directions. Even the molecules of air are large enough to scatter
light; in 1871, Lord Rayleigh showed that this accounts for the blue sky.
(Since then, molecular scattering has been called
“Rayleigh
scattering.”)

SNEL'S LAW gives the quantitative change of direction of a ray of light
in passing from one medium to another. The product n sin z
is the same on both sides of a plane interface between two media, where
n is the local refractive index, and z is the local angle
the ray makes with the normal to the interface.
(See the refraction page.)

In the curved atmosphere, Snel's law becomes nR sin z = constant,
where R is distance from the local center of curvature;
see the page especially devoted to this
refractive invariant.

but is very similar to its 1962 predecessor, and to the 1958 ICAO Standard
Atmosphere in the lower parts that are important for refraction.
(Further details are available from
NSSDC,
NASA,
Digital Dutch's calculator,
the
AMS
Glossary,
and other sources.)
Its most important property, for present purposes, is its constant
lapse rate of 6.5 K/km.
(I have a page
that shows its temperature profile.)

This “model atmosphere” is a highly idealized version of the average of
many measurements made in the real atmosphere.
Thus, it lacks the fine structure that is always present in the real
world.

SUPERIOR MIRAGE: "Superior" means "higher"; this is the mirage in which
the inverted image is above the normal one. These are somewhat
uncommon, and are associated with ducting.

T

TERRESTRIAL REFRACTION: The displacement of terrestrial objects from their
geometric directions by atmospheric
refraction. You may not notice
it, but it is a major headache for geodesists and surveyors.
Cf. astronomical refraction.

THERMAL INVERSION: On the average, the temperature in the lower atmosphere
decreases with increasing height.
(The average gradient is about 6.5 K
per kilometer.) A region in which the warmer air lies above the colder
air is said to have an “inverted” temperature gradient, and is called a
“thermal inversion,” or “inversion layer.” A thermal inversion is
required to produce a
superior mirage.

TOWERING: Abnormal vertical stretching of the image of a distant
object; the opposite of stooping.
Towering and stooping are refraction phenomena that distort but do not
invert images; hence, they are not mirages.
(See the table of
refraction phenomena,
and the
simulations.)

U

V

W

X

Y

Z

ZENITH: The point in the sky straight overhead (i.e., the direction
“straight up”). The direction to the zenith is perpendicular to the
astronomical horizon.

ZENITH DISTANCE: The angular distance of an object from the zenith.
The zenith distance of an object is the complement of its
altitude.
The zenith distance of the
astronomical horizon
is 90 degrees.